Right so, I'm afraid you did miss it, but having multiple abilities is a no-go. I find that abilities are a nice way to create difference between two pokémon of the same species, this wouldn't really work if every pokémon had all of their abilities.

A nice way you could make synchronize work perhaps, would be the creation of a mental link or just a psychic wave. Burn and Freeze for example, aren't going to literally set you on fire or encase you in a block of ice. Burn would instead be burn wounds, which would be quite painful and in that way hamper someone. A pokémon with synchronize would, for example, be able to create a mental link through which it would share this pain with the person who inflicted the wound. Trace meanwhile, is very dependent on the ability it copies, but I'd like to think you should be able to make it work in a similar fashion.